Heat transfer problem is one of the main challenges in the design process of turbomachinery components for aeronautic applications. Good prediction capabilities are required to estimate metal temperatures, specially in those regions where the working fluid reaches temperatures near to the material melting point. In this context, it is common to perform multi-physics simulations involving different solvers. Special care must be taken at the interfaces between the several domains to avoid non-physical solutions. Concretely speaking, the coupling process between a thermal code (discretized heat diffusion equation solver) and a fluid network (low fidelity models representing air flows) is studied. Several non-physical boundary conditions examples are provided. The models are solved using an in-house thermal code called Saturn. The effects both in the results and in the convergence process are described. Non-physical boundary conditions provoke instabilities in the flow direction at some parts of the fluid network. A method to analyze the compatibility and convergence of the coupled problem is described and used in the examples. Also, some heuristics to achieve converge in the ill-posed models are commented.